Subject statistics

meanAge sdAge minAge maxAge n numFemales
21.98 2.172 18 25.42 30 16

Confirmatory analyses: Experiment 2

Frequency-learning task

Frequency task accuracy

meanAcc sdAcc
0.9823 0.132
meanAcc sdAcc
0.9552 0.2069

Frequency accuracy mixed-effects model: New items

## Fitting 2 (g)lmer() models:
## [..]
Observations 960
Dependent variable freqAcc
Type Mixed effects generalized linear model
Family binomial
Link logit
AIC 181.85
BIC 211.05
Fixed Effects
Est. S.E. z val. p
(Intercept) 4.70 0.65 7.26 0.00
block1 -0.07 0.31 -0.23 0.82
Random Effects
Group Parameter Std. Dev.
item re2.block1 0.55
item.1 (Intercept) 0.71
sub re1.block1 0.74
sub.1 (Intercept) 0.48
Grouping Variables
Group # groups ICC
item 32 0.06
sub 30 0.10

Frequency accuracy mixed-effects model: Repeated items

## Fitting 4 (g)lmer() models:
## [....]
Observations 1920
Dependent variable freqAcc
Type Mixed effects generalized linear model
Family binomial
Link logit
AIC 585.92
BIC 719.36
Pseudo-R² (fixed effects) 0.42
Pseudo-R² (total) 0.86
Fixed Effects
Est. S.E. z val. p
(Intercept) 6.22 0.99 6.28 0.00
block1 0.95 1.00 0.95 0.34
appearanceCountScaled 2.81 0.76 3.72 0.00
block1:appearanceCountScaled 1.09 0.76 1.43 0.15
Random Effects
Group Parameter Std. Dev.
item (Intercept) 1.11
item block1 0.38
item appearanceCountScaled 0.51
item block1:appearanceCountScaled 0.47
sub (Intercept) 1.58
sub block1 1.87
sub appearanceCountScaled 1.09
sub block1:appearanceCountScaled 1.32
Grouping Variables
Group # groups ICC
item 32 0.18
sub 30 0.36

Frequency task reaction times:

Frequency reaction times mixed-effects model: Repeated items

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
Observations 1834
Dependent variable freqRT
Type Mixed effects linear regression
AIC -374.91
BIC -237.05
Pseudo-R² (fixed effects) 0.05
Pseudo-R² (total) 0.41
Fixed Effects
Est. S.E. t val. d.f. p
(Intercept) 0.83 0.03 33.22 32.77 0.00
appearanceCountScaled -0.05 0.01 -6.35 29.63 0.00
block1 -0.03 0.01 -1.94 28.95 0.06
appearanceCountScaled:block1 0.00 0.01 0.12 36.30 0.91
p values calculated using Satterthwaite d.f.
Random Effects
Group Parameter Std. Dev.
item (Intercept) 0.04
item appearanceCountScaled 0.01
item block1 0.01
item appearanceCountScaled:block1 0.01
sub (Intercept) 0.13
sub appearanceCountScaled 0.03
sub block1 0.07
sub appearanceCountScaled:block1 0.02
Residual 0.20
Grouping Variables
Group # groups ICC
item 32 0.02
sub 30 0.29

Plot: Frequency task reaction times

Explicit frequency reports

Explicit frequency reports mixed-effects model

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
Observations 960
Dependent variable memFreqRespErrorMagnitude
Type Mixed effects linear regression
AIC 2778.48
BIC 2866.08
Pseudo-R² (fixed effects) 0.01
Pseudo-R² (total) 0.31
Fixed Effects
Est. S.E. t val. d.f. p
(Intercept) 1.24 0.08 16.51 31.98 0.00
freqCondFactor1 -0.08 0.11 -0.81 31.26 0.43
block2 -0.03 0.10 -0.34 28.23 0.74
freqCondFactor1:block2 0.24 0.11 2.24 28.75 0.03
p values calculated using Satterthwaite d.f.
Random Effects
Group Parameter Std. Dev.
item (Intercept) 0.12
item freqCondFactor1 0.13
sub (Intercept) 0.32
sub freqCondFactor1 0.51
sub block2 0.45
sub freqCondFactor1:block2 0.48
Residual 0.91
Grouping Variables
Group # groups ICC
item 32 0.02
sub 30 0.11
block freqCondFactor meanError
1 1 1.158
1 5 1.325
2 1 1.35
2 5 1.054

Plot: Frequency report distributions

Memory accuracy

Memory accuracy mixed-effects model

## Fitting 4 (g)lmer() models:
## [....]
Observations 960
Dependent variable memAcc
Type Mixed effects generalized linear model
Family binomial
Link logit
AIC 1189.73
BIC 1248.14
Fixed Effects
Est. S.E. z val. p
(Intercept) -0.79 0.17 -4.64 0.00
freqCondFactor1 -0.07 0.07 -0.99 0.32
block1 -0.23 0.09 -2.58 0.01
freqCondFactor1:block1 0.05 0.08 0.65 0.51
Random Effects
Group Parameter Std. Dev.
item re2.freqCondFactor1_by_block1 0.00
item.1 re2.block1 0.20
item.2 re2.freqCondFactor1 0.00
item.3 (Intercept) 0.42
sub re1.freqCondFactor1_by_block1 0.19
sub.1 re1.block1 0.18
sub.2 re1.freqCondFactor1 0.00
sub.3 (Intercept) 0.72
Grouping Variables
Group # groups ICC
item 32 0.00
sub 30 0.01

Bayesian analysis of memory

Model comparison without frequency condition interaction

## [1] 18.46007

Model comparison with full model

## [1] 297525203

Full brms accuracy model

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## Chain 4:
##  Family: bernoulli 
##   Links: mu = logit 
## Formula: memAcc ~ freqCondFactor * block + (freqCondFactor * block | sub) + (freqCondFactor * block | item) 
##    Data: memData (Number of observations: 960) 
## Samples: 4 chains, each with iter = 1e+05; warmup = 50000; thin = 1;
##          total post-warmup samples = 2e+05
## 
## Group-Level Effects: 
## ~item (Number of levels: 32) 
##                                             Estimate Est.Error l-95% CI
## sd(Intercept)                                   0.44      0.20     0.06
## sd(freqCondFactor5)                             0.35      0.23     0.02
## sd(block2)                                      0.39      0.25     0.02
## sd(freqCondFactor5:block2)                      0.33      0.25     0.01
## cor(Intercept,freqCondFactor5)                  0.21      0.41    -0.64
## cor(Intercept,block2)                          -0.32      0.42    -0.91
## cor(freqCondFactor5,block2)                    -0.05      0.43    -0.82
## cor(Intercept,freqCondFactor5:block2)          -0.04      0.44    -0.82
## cor(freqCondFactor5,freqCondFactor5:block2)    -0.15      0.45    -0.88
## cor(block2,freqCondFactor5:block2)             -0.10      0.45    -0.85
##                                             u-95% CI Rhat Bulk_ESS
## sd(Intercept)                                   0.86 1.00    37518
## sd(freqCondFactor5)                             0.85 1.00    45030
## sd(block2)                                      0.95 1.00    44569
## sd(freqCondFactor5:block2)                      0.93 1.00    70221
## cor(Intercept,freqCondFactor5)                  0.87 1.00   111234
## cor(Intercept,block2)                           0.64 1.00    81778
## cor(freqCondFactor5,block2)                     0.77 1.00    98215
## cor(Intercept,freqCondFactor5:block2)           0.78 1.00   170443
## cor(freqCondFactor5,freqCondFactor5:block2)     0.75 1.00   138384
## cor(block2,freqCondFactor5:block2)              0.77 1.00   139449
##                                             Tail_ESS
## sd(Intercept)                                  34415
## sd(freqCondFactor5)                            74162
## sd(block2)                                     75319
## sd(freqCondFactor5:block2)                     87993
## cor(Intercept,freqCondFactor5)                114952
## cor(Intercept,block2)                         121522
## cor(freqCondFactor5,block2)                   131247
## cor(Intercept,freqCondFactor5:block2)         140165
## cor(freqCondFactor5,freqCondFactor5:block2)   150594
## cor(block2,freqCondFactor5:block2)            160698
## 
## ~sub (Number of levels: 30) 
##                                             Estimate Est.Error l-95% CI
## sd(Intercept)                                   0.85      0.20     0.51
## sd(freqCondFactor5)                             0.29      0.21     0.01
## sd(block2)                                      0.47      0.29     0.03
## sd(freqCondFactor5:block2)                      0.49      0.34     0.02
## cor(Intercept,freqCondFactor5)                 -0.31      0.42    -0.91
## cor(Intercept,block2)                           0.02      0.39    -0.69
## cor(freqCondFactor5,block2)                     0.06      0.44    -0.78
## cor(Intercept,freqCondFactor5:block2)          -0.14      0.40    -0.82
## cor(freqCondFactor5,freqCondFactor5:block2)    -0.06      0.45    -0.84
## cor(block2,freqCondFactor5:block2)             -0.17      0.45    -0.88
##                                             u-95% CI Rhat Bulk_ESS
## sd(Intercept)                                   1.29 1.00    75441
## sd(freqCondFactor5)                             0.78 1.00    61637
## sd(block2)                                      1.08 1.00    35850
## sd(freqCondFactor5:block2)                      1.26 1.00    45358
## cor(Intercept,freqCondFactor5)                  0.64 1.00   132031
## cor(Intercept,block2)                           0.77 1.00   116900
## cor(freqCondFactor5,block2)                     0.83 1.00    58179
## cor(Intercept,freqCondFactor5:block2)           0.68 1.00   152279
## cor(freqCondFactor5,freqCondFactor5:block2)     0.78 1.00   100650
## cor(block2,freqCondFactor5:block2)              0.74 1.00    91294
##                                             Tail_ESS
## sd(Intercept)                                 117596
## sd(freqCondFactor5)                            83216
## sd(block2)                                     64148
## sd(freqCondFactor5:block2)                     74750
## cor(Intercept,freqCondFactor5)                138442
## cor(Intercept,block2)                         111621
## cor(freqCondFactor5,block2)                   108641
## cor(Intercept,freqCondFactor5:block2)         136843
## cor(freqCondFactor5,freqCondFactor5:block2)   133967
## cor(block2,freqCondFactor5:block2)            134745
## 
## Population-Level Effects: 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept                 -1.05      0.24    -1.55    -0.59 1.00    81124
## freqCondFactor5            0.02      0.24    -0.46     0.50 1.00   125275
## block2                     0.34      0.26    -0.17     0.84 1.00   119243
## freqCondFactor5:block2     0.25      0.34    -0.40     0.91 1.00   116265
##                        Tail_ESS
## Intercept                111787
## freqCondFactor5          140593
## block2                   131608
## freqCondFactor5:block2   136449
## 
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample 
## is a crude measure of effective sample size, and Rhat is the potential 
## scale reduction factor on split chains (at convergence, Rhat = 1).

Plot: Effects of frequency condition and block on memory

Plot: Effects of frequency condition on memory (individual subjects)

Relation between learning environmental statistics and memory encoding

Memory benefit mixed effects model

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
Observations 59
Dependent variable memBenefitIndex
Type Mixed effects linear regression
AIC 177.27
BIC 189.74
Pseudo-R² (fixed effects) 0.05
Pseudo-R² (total) 0.09
Fixed Effects
Est. S.E. t val. d.f. p
(Intercept) 0.18 0.13 1.43 27.69 0.16
freqDistScaled 0.24 0.15 1.62 52.84 0.11
block1 0.04 0.12 0.32 27.56 0.75
freqDistScaled:block1 -0.06 0.15 -0.43 50.78 0.67
p values calculated using Satterthwaite d.f.
Random Effects
Group Parameter Std. Dev.
sub (Intercept) 0.20
Residual 0.92
Grouping Variables
Group # groups ICC
sub 30 0.05

Plot: Relation between frequency distance and memory benefit

Item-level relation between frequency reports and memory mixed-effects model

## Fitting 4 (g)lmer() models:
## [....]
Observations 960
Dependent variable memAcc
Type Mixed effects generalized linear model
Family binomial
Link logit
AIC 1200.41
BIC 1317.22
Pseudo-R² (fixed effects) 0.03
Pseudo-R² (total) 0.24
Fixed Effects
Est. S.E. z val. p
(Intercept) -0.81 0.17 -4.65 0.00
memFreqRespScaled 0.27 0.09 2.94 0.00
block1 -0.24 0.10 -2.45 0.01
memFreqRespScaled:block1 0.02 0.09 0.16 0.87
Random Effects
Group Parameter Std. Dev.
item (Intercept) 0.46
item memFreqRespScaled 0.13
item block1 0.24
item memFreqRespScaled:block1 0.16
sub (Intercept) 0.72
sub memFreqRespScaled 0.12
sub block1 0.16
sub memFreqRespScaled:block1 0.16
Grouping Variables
Group # groups ICC
item 32 0.05
sub 30 0.13

Plot: Effects of frequency report on memory accuracy

Exploratory analyses: Comparison of E1 and E2

include grandMeanPaAcc sdPaAcc minPaAcc
0 0 NA 0
1 0.959 0.05577 0.8125

Frequency-learning task

Frequency-learning accuracy

Frequency accuracy mixed-effects model: New items

## Fitting 4 (g)lmer() models:
## [....]
Observations 1888
Dependent variable freqAcc
Type Mixed effects generalized linear model
Family binomial
Link logit
AIC 362.87
BIC 418.31
Pseudo-R² (fixed effects) 0.01
Pseudo-R² (total) 0.18
Fixed Effects
Est. S.E. z val. p
(Intercept) 4.58 0.44 10.51 0.00
block1 -0.20 0.22 -0.90 0.37
exp1 -0.01 0.21 -0.02 0.98
block1:exp1 -0.13 0.20 -0.63 0.53
Random Effects
Group Parameter Std. Dev.
sub (Intercept) 0.71
sub.1 re1.block1 0.64
item (Intercept) 0.38
item.1 re2.block1 0.49
item.2 re2.exp1 0.14
item.3 re2.block1_by_exp1 0.00
Grouping Variables
Group # groups ICC
sub 59 0.11
item 32 0.09

Frequency accuracy mixed-effects model: Repeated items

## Fitting 8 (g)lmer() models:
## [........]
Observations 3776
Dependent variable freqAcc
Type Mixed effects generalized linear model
Family binomial
Link logit
AIC 1234.91
BIC 1359.64
Pseudo-R² (fixed effects) 0.36
Pseudo-R² (total) 0.50
Fixed Effects
Est. S.E. z val. p
(Intercept) 4.55 0.26 17.28 0.00
block1 -0.54 0.20 -2.76 0.01
appearanceCountScaled 1.35 0.17 7.89 0.00
exp1 0.08 0.21 0.39 0.70
block1:appearanceCountScaled -0.11 0.16 -0.69 0.49
block1:exp1 -0.31 0.20 -1.57 0.12
appearanceCountScaled:exp1 0.22 0.16 1.39 0.16
block1:appearanceCountScaled:exp1 -0.33 0.15 -2.15 0.03
Random Effects
Group Parameter Std. Dev.
sub (Intercept) 0.83
sub.1 re1.block1 0.77
sub.2 re1.appearanceCountScaled 0.57
sub.3 re1.block1_by_appearanceCountScaled 0.39
item (Intercept) 0.54
item.1 re2.block1 0.00
item.2 re2.appearanceCountScaled 0.18
item.3 re2.exp1 0.31
item.4 re2.block1_by_appearanceCountScaled 0.19
item.5 re2.block1_by_exp1 0.00
item.6 re2.appearanceCountScaled_by_exp1 0.00
item.7 re2.block1_by_appearanceCountScaled_by_exp1 0.00
Grouping Variables
Group # groups ICC
sub 59 0.12
item 32 0.11

Plot: Frequency task accuracy

Frequency task reaction times

Frequency task reaction times mixed-effects model

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
Observations 3587
Dependent variable freqRT
Type Mixed effects linear regression
AIC -801.08
BIC -671.19
Pseudo-R² (fixed effects) 0.05
Pseudo-R² (total) 0.32
Fixed Effects
Est. S.E. t val. d.f. p
(Intercept) 0.82 0.02 47.47 70.54 0.00
appearanceCountScaled -0.05 0.01 -8.43 55.99 0.00
block1 -0.02 0.01 -1.62 55.51 0.11
exp1 -0.01 0.02 -0.55 57.19 0.59
appearanceCountScaled:block1 0.00 0.00 0.25 54.46 0.81
appearanceCountScaled:exp1 0.00 0.01 0.50 55.98 0.62
block1:exp1 0.01 0.01 1.09 56.50 0.28
appearanceCountScaled:block1:exp1 0.00 0.00 0.13 54.46 0.90
p values calculated using Satterthwaite d.f.
Random Effects
Group Parameter Std. Dev.
sub (Intercept) 0.12
sub.1 re1.appearanceCountScaled 0.04
sub.2 re1.block1 0.07
sub.3 re1.appearanceCountScaled_by_block1 0.02
item (Intercept) 0.04
item.1 re2.appearanceCountScaled 0.00
item.2 re2.block1 0.00
item.3 re2.exp1 0.01
item.4 re2.appearanceCountScaled_by_block1 0.00
item.5 re2.appearanceCountScaled_by_exp1 0.00
item.6 re2.block1_by_exp1 0.01
item.7 re2.appearanceCountScaled_by_block1_by_exp1 0.00
Residual 0.20
Grouping Variables
Group # groups ICC
sub 59 0.23
item 32 0.02

Plot: Frequency task reaction times

Explicit frequency reports

Frequency error mixed-effects model

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
Observations 1920
Dependent variable memFreqRespErrorMagnitude
Type Mixed effects linear regression
AIC 5616.07
BIC 5732.83
Pseudo-R² (fixed effects) 0.01
Pseudo-R² (total) 0.19
Fixed Effects
Est. S.E. t val. d.f. p
(Intercept) 1.21 0.06 19.37 69.01 0.00
freqCondFactor1 -0.02 0.06 -0.33 66.09 0.74
exp1 -0.02 0.06 -0.27 61.38 0.79
block1 0.02 0.03 0.72 56.87 0.48
freqCondFactor1:exp1 -0.05 0.06 -0.93 58.21 0.35
freqCondFactor1:block1 -0.09 0.03 -2.70 55.52 0.01
exp1:block1 0.01 0.03 0.17 43.54 0.87
freqCondFactor1:exp1:block1 0.03 0.03 1.06 55.44 0.29
p values calculated using Satterthwaite d.f.
Random Effects
Group Parameter Std. Dev.
sub (Intercept) 0.40
sub.1 re1.freqCondFactor1 0.40
sub.2 re1.block1 0.19
sub.3 re1.freqCondFactor1_by_block1 0.19
item (Intercept) 0.15
item.1 re2.freqCondFactor1 0.14
item.2 re2.exp1 0.09
item.3 re2.block1 0.00
item.4 re2.freqCondFactor1_by_exp1 0.06
item.5 re2.freqCondFactor1_by_block1 0.00
item.6 re2.exp1_by_block1 0.05
item.7 re2.freqCondFactor1_by_exp1_by_block1 0.00
Residual 0.92
Grouping Variables
Group # groups ICC
sub 60 0.12
item 32 0.12

Plot: Frequency report distributions

Memory test

Memory accuracy mixed-effects model

## Fitting 8 (g)lmer() models:
## [........]
Observations 1920
Dependent variable memAcc
Type Mixed effects generalized linear model
Family binomial
Link logit
AIC 2354.69
BIC 2465.89
Pseudo-R² (fixed effects) 0.04
Pseudo-R² (total) 0.22
Fixed Effects
Est. S.E. z val. p
(Intercept) -0.74 0.13 -5.52 0.00
freqCondFactor1 -0.26 0.07 -3.93 0.00
block1 -0.23 0.06 -3.59 0.00
exp1 0.06 0.12 0.52 0.60
freqCondFactor1:block1 0.06 0.06 0.92 0.36
freqCondFactor1:exp1 -0.18 0.06 -3.08 0.00
block1:exp1 0.01 0.06 0.16 0.87
freqCondFactor1:block1:exp1 -0.00 0.06 -0.07 0.95
Random Effects
Group Parameter Std. Dev.
sub (Intercept) 0.78
sub.1 re1.freqCondFactor1 0.18
sub.2 re1.block1 0.18
sub.3 re1.freqCondFactor1_by_block1 0.23
item (Intercept) 0.38
item.1 re2.freqCondFactor1 0.17
item.2 re2.block1 0.14
item.3 re2.exp1 0.15
item.4 re2.freqCondFactor1_by_block1 0.00
item.5 re2.freqCondFactor1_by_exp1 0.00
item.6 re2.block1_by_exp1 0.04
item.7 re2.freqCondFactor1_by_block1_by_exp1 0.00
Grouping Variables
Group # groups ICC
sub 60 0.14
item 32 0.01

Plot: Effects of frequency condition and block on memory

Plot: Effects of frequency condition on memory (individual subjects)

Relation between learning environmental statistics and memory encoding

Memory benefit mixed-effects model

## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
Observations 117
Dependent variable memBenefitIndex
Type Mixed effects linear regression
AIC 350.64
BIC 378.26
Pseudo-R² (fixed effects) 0.07
Pseudo-R² (total) 0.10
Fixed Effects
Est. S.E. t val. d.f. p
(Intercept) 0.37 0.09 4.23 52.25 0.00
freqDistScaled 0.10 0.10 0.95 105.09 0.34
block1 0.01 0.09 0.07 52.22 0.94
exp1 0.17 0.09 1.90 52.25 0.06
freqDistScaled:block1 -0.12 0.10 -1.23 103.06 0.22
freqDistScaled:exp1 -0.11 0.10 -1.11 105.09 0.27
block1:exp1 -0.03 0.09 -0.30 52.22 0.77
freqDistScaled:block1:exp1 -0.07 0.10 -0.66 103.06 0.51
p values calculated using Satterthwaite d.f.
Random Effects
Group Parameter Std. Dev.
sub (Intercept) 0.15
Residual 0.92
Grouping Variables
Group # groups ICC
sub 60 0.03

Plot: Relation between frequency distance and memory benefit

Item-level relation between frequency reports and memory mixed-effects model

## Fitting 8 (g)lmer() models:
## [........]
Observations 1920
Dependent variable memAcc
Type Mixed effects generalized linear model
Family binomial
Link logit
AIC 2333.71
BIC 2444.91
Pseudo-R² (fixed effects) 0.06
Pseudo-R² (total) 0.23
Fixed Effects
Est. S.E. z val. p
(Intercept) -0.73 0.13 -5.55 0.00
memFreqRespScaled 0.41 0.06 6.37 0.00
block1 -0.21 0.06 -3.48 0.00
exp1 0.06 0.11 0.52 0.60
memFreqRespScaled:block1 0.00 0.06 0.06 0.95
memFreqRespScaled:exp1 0.16 0.06 2.76 0.01
block1:exp1 0.01 0.06 0.19 0.85
memFreqRespScaled:block1:exp1 0.00 0.06 0.02 0.99
Random Effects
Group Parameter Std. Dev.
sub (Intercept) 0.77
sub.1 re1.memFreqRespScaled 0.00
sub.2 re1.block1 0.16
sub.3 re1.memFreqRespScaled_by_block1 0.16
item (Intercept) 0.37
item.1 re2.memFreqRespScaled 0.15
item.2 re2.block1 0.09
item.3 re2.exp1 0.12
item.4 re2.memFreqRespScaled_by_block1 0.00
item.5 re2.memFreqRespScaled_by_exp1 0.00
item.6 re2.block1_by_exp1 0.09
item.7 re2.memFreqRespScaled_by_block1_by_exp1 0.00
Grouping Variables
Group # groups ICC
sub 60 0.14
item 32 0.00

Plot: Effects of frequency report on memory accuracy